

The group \(/() = \hat{K}_a/(\hat{K}_d \hat{H})\)  in (REF ) appears frequently in this problem.
The depletion length \(\hat{L}_d = \hat{K}_a/\hat{K}_d\)  [1]} corresponds to the depth into the liquid necessary to balance the adsorption and desorption fluxes between the interface and the bulk, at equilibrium.
Hence, the group \(/()\)  compares \(\hat{L}_d\)  to the channel height \(\hat{H}\) .
The drag reduction (REF ) becomes
\( {DR} = \frac{\Delta p_R - \Delta p}{\Delta p_R - \Delta p_U},\) 
